Chapter 21: Square Roots: Situation 15 From the MACMTL–CPTM Situations Project

A teacher asked her students to sketch the graph of $f(x)=-x.$⁠. A student responded, “That's impossible! You can’t take the square root of a negative number!”

This Situation addresses several key concepts that occur frequently in school mathematics: additive inverse, negative numbers, function, domain, and range. Because the symbol “” has multiple interpretations, it is important to distinguish between a negative number and the additive inverse (i.e., opposite) of a number.¹ Moreover, the domain over which a function is defined determines its range, and a table of values provides an example to illustrate the relationship between domain and range. For a set of points with coordinates (x , f (x )) to define the graph of a function, each first coordinate, x , must correspond to a unique second coordinate, f (x ). A graphical representation highlights the univalent relationship between x and f (x ).